Let's now look at a common example of adiabatic compression- the compression stroke in a gasoline engine. We will make a few simplifying assumptions: that the uncompressed volume of the cylinder is 1000cc's (one liter), that the gas within is nearly pure nitrogen (thus a diatomic gas with five degrees of freedom and so = 7/5), and that the compression ratio of the engine is 10:1 (that is, the 1000 cc volume of uncompressed gas will compress down to 100 cc when the piston goes from bottom to top). The uncompressed gas is at approximately room temperature and pressure (a warm room temperature of ~27 degC or 300 K, and a pressure of 1 bar ~ 100,000 Pa, or about 14.7 PSI, or typical sea-level atmospheric pressure).
so our adiabatic constant for this experiment is about 1.58 billion.
The gas is now compressed to a 100cc volume (we will assume this happens quickly enough that no heat can enter or leave the gas). The new volume is 100 ccs, but the constant for this experiment is still 1.58 billion:
so solving for P:
or about 362 PSI or 24.5 atm. Note that this pressure increase is more than a simple 10:1 compression ratio would indicate; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.
We can solve for the temperature of the compressed gas in the engine cylinder as well, using the ideal gas law. Our initial conditions are 100,000 pa of pressure, 1000 cc volume, and 300 K of temperature, so our experimental constant is:
We know the compressed gas has V = 100 cc and P = 2.50E6 pascals, so we can solve for temperature by simple algebra:
That's a final temperature of 751 K, or 477 °C, or 892 °F, well above the ignition point of many fuels. This is why a high compression engine requires fuels specially formulated to not self-ignite (which would cause engine knocking when operated under these conditions of temperature and pressure), or that a supercharger and intercooler to provide a lower temperature at the same pressure would be advantageous. A diesel engine operates under even more extreme conditions, with compression ratios of 20:1 or more being typical, in order to provide a very high gas temperature which ensures immediate ignition of injected fuel.

Here ya go guy's...the science behind it. Theory works to get you something useful in practical applications but stray too far from theory and the practical won't last too long!